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17Oct/130

Logical proof that affirmative action kills academic integrity

I've argued that at a logical level, affirmative action kills academic integrity - something that I would assume (and hope) that universities strive for.

So the narrative would go something like this:
If a university admits academically incapable students, then institutional academic integrity declines
Universities want to maintain academic integrity
Academic capability is race neutral
If a university implements an affirmative action policy, then either academically capable applicants get admitted or (inclusive usage) academically incapable applicants get admitted
If a university does not implement an affirmative action policy, then academically capable applicants get admitted
If a university implements an affirmative action policy, then academic capability is not race neutral

Conclusion: If a university wants to maintain institutional academic integrity, then they will not want to implement an affirmative action policy.

I'm quite the fan of propositional logic. Given that, the following shows the symbolized atomic elements that build the propositions, followed by the symbolized propositions:

Symbolized propositions:

  • A) Universities admitting academically capable students
  • B) Universities implement affirmative action policies
  • C) Institutional academic integrity declines // Universities want academic integrity to decline
  • D) Academic capability is race neutral

The symbolized propositions and conclusion:

~A -> C
~C
D
B -> (A v ~A)
~B -> A
B -> ~D
=========
~C -> ~B

Assumptions
Before I bust out the truth table, let me describe, for those playing along at home who will be seeing this for the first time, how this thing works.

Essentially, the truth table shows the logical outcomes based on all possible combinations of truth values for the propositions (which have been symbolized).

Implied assumptions
Clearly there are some things that we know are true, or we should expect to be true.

  1. We should expect that universities don't want academic integrity to decline (we operate under the assumption that C should be false, or ~C)
  2. We should expect that academic integrity is linked to academic capability of the students (not symbolized in this case).
  3. Academic capability is race neutral (D should be true). Basically, you can be be black, white, tan, red, or rainbow colored, and still have the ability to be academically capable.

So then the question is: Should affirmative action be implemented (B is true) or not (B is false or ~B)? The argument's conclusion that a necessary condition of maintaining academic integrity (~C) is that affirmative action not be implemented (~B).

What we are looking for is what condition(s) where all the propositions are true, as well as the conclusion (which will be the last column).

So here is the truth table in all its glory:

Condition A B C D ~A->C ~C D B->(A|~A) ~B->A B->~D ~C->~B
1 T T T T T F T T T F T
2 T T T F T F F T T T T
3 T T F T T T T T T F F
4 T T F F T T F T T T F
5 T F T T T F T T T T T
6 T F T F T F F T T T T
7 T F F T T T T T T T T
8 T F F F T T F T T T T
9 F T T T T F T T T F T
10 F T T F T F F T T T T
11 F T F T F T T T T F F
12 F T F F F T F T T T F
13 F F T T T F T T F T T
14 F F T F T F F T F T T
15 F F F T F T T T F T T
16 F F F F F T F T F T T

Take a look at condition 7. We see this is the only condition where all the propositions evaluate to true, as well as the conclusion.
You'll also note that this is a valid argument, as there is no situation where the conclusion evaluates to true while all the propositions evaluate to false.

Further discussion
This is a relatively simple argument. There are those who might try to bring up the "racial diversity is good" argument. Indeed, this argument could be redrawn to take this into account, and the propositions and table be redone. However, think of this: What is the point of a university? I argue that it's to provide advanced education, and that racial diversity for the sake of racial diversity at the expense of academic integrity is bad.

Such a truth table could be drawn up with all its propositions to handle a more advanced situation where the implied assumptions are questioned, however, I would regard such challenges to applied assumptions to be borked.

   
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